Account for useful and dissipated transfers without losing energy from the total.
Method and worked examples
Choose a system and account for energy entering, leaving and changing form. When only gravity transfers between kinetic and gravitational potential energy, Ek+ Ep is constant. With friction, mechanical energy can decrease while total energy is conserved through internal-energy increases and other transfers. Do not silently discard a heating term or assume every object starts from rest.
Average power is P=tE, or the rate of doing work. Efficiency is useful output divided by total input, with matching energy units or matching power units. Multiply by 100 for a percentage. A Sankey-style balance can be solved arithmetically: input equals all outputs in a steady device without net storage. Define the useful output for the stated purpose.
Example 1
A ball drops from rest through 5.0m with negligible drag. Use g=9.8m/s2. Find speed after the drop.
mgh= ½mv2, so v=√2gh=√98=9.90m/s. Mass cancels; the stated model neglects drag.
Example 2
A machine takes 500J in 2.0s and delivers 350J usefully. Find input power and efficiency.
Pin=2.0500=250W. Efficiency =500350×100=70%. Other outputs total 150J.
Watch out:It has transferred into outputs less useful for the chosen purpose, commonly heating. Total energy is still conserved.
18. Energy conservation, power and efficiency | Year 11 Physics | Ascent Arcade